What is the formula for mechanical work?

W = F × d × cos θ, where W is work (joules), F is the magnitude of the force (newtons), d is the displacement (meters), and θ is the angle between the force vector and the displacement vector.

What does a negative work value mean?

Negative work means the force opposes the direction of motion. For example, friction does negative work on a sliding object because it acts opposite to displacement (θ = 180°, cos 180° = −1).

What happens when θ = 90°?

When the force is perpendicular to the displacement (θ = 90°), cos 90° = 0, so no work is done. A classic example is a person carrying a box horizontally — the upward support force does zero work.

What units does this calculator support?

Force: Newtons (N), kilonewtons (kN), pounds-force (lbf), kilogram-force (kgf). Distance: meters (m), kilometers (km), centimeters (cm), feet (ft), inches (in). Output: joules (J), kilojoules (kJ), kilowatt-hours (kWh), foot-pounds (ft·lbf), calorie (cal).

Is work a scalar or vector quantity?

Work is a scalar — it has magnitude but no direction. Even though force and displacement are vectors, their dot product (W = F⃗ · d⃗) yields a scalar value.

How is this related to the work-energy theorem?

The work-energy theorem states that the net work done on an object equals the change in its kinetic energy (W_net = ΔKE). This calculator computes the work done by a single force; for net work, sum the contributions from all forces.

Work Calculator

Name: Work Calculator
Availability: InStock
Author: Nham Vu

Calculate mechanical work done by a force using W = F × d × cos θ with instant unit conversion.

Inputs

W = F × d × cos θ

Force (F)

Distance (d)

Angle θ between force and motion

deg

0° (same direction) 90° (no work) 180° (opposite)

Output unit

Result

Enter values and click Calculate Work

Common Scenarios

Push box 5 m with 100 N (parallel) 500 J

Pull rope at 30°, 50 N over 3 m ~130 J

Carry box horizontally (force upward, 90°) 0 J

Friction opposing motion (180°) −120 J

Summary

Calculate mechanical work done by a force using W = F × d × cos θ with instant unit conversion.

How it works

Enter the force applied to the object.
Enter the displacement (distance) the object moves.
Enter the angle between the force vector and the direction of motion.
Select your preferred units for force, distance, and energy.
The calculator instantly applies W = F × d × cos θ and displays the result.
A negative result means work is done against the motion (e.g., friction).

Use cases

Physics homework and exam preparation.
Engineering problems involving force and displacement.
Checking whether a force is doing positive or negative work on an object.
Converting work results between joules, kilowatt-hours, foot-pounds, and more.
Understanding energy transfer in mechanical systems.
Teaching or demonstrating the work-energy theorem in classrooms.
Estimating effort required to push or pull an object along a surface.
Analyzing inclined-plane and pulley scenarios.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu